lyzzy7
multiple choice question! please help!
Suppose y varies directly with x, and y = 14 when x = –4. What is the value of y when x = –6?
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jim_thompson5910
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y varies directly with x
means that
y = kx
jim_thompson5910
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when x = -4, y is y = 14
so
y = kx
turns into
14 = k*(-4)
jim_thompson5910
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solve for k and tell me what you get
lyzzy7
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-3.5, But I think Im wrong..
jim_thompson5910
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you're correct
jim_thompson5910
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so
y = kx
turns into
y = -3.5x
jim_thompson5910
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now they want to know the value of y when x = -6
jim_thompson5910
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so
y = -3.5x
y = -3.5(-6)
y = ???
lyzzy7
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21.
lyzzy7
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thank yoouuu!:))
jim_thompson5910
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nailed it
lyzzy7
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can you walk me through this one too?
Suppose y varies directly with x, and y = 25 when x = 140. What is the value of x when y = 36?
jim_thompson5910
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y varies directly with x
means what
lyzzy7
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y=kx
jim_thompson5910
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we're given x = 140 and y = 25
so
y = kx
becomes
25 = k*140
jim_thompson5910
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so k = ____
lyzzy7
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.18
jim_thompson5910
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I would use more decimal places for k. I'm going to use k = 0.17857
so
y = kx
becomes
y = 0.17857x
Now plug in y = 36 and solve for x
y = 0.17857x
36 = 0.17857x
36/ 0.17857 = x
201.601613 = x
x = 201.601613
now round to the nearest tenth to get 201.6
this is the same as 201 and 3/5 or the improper fraction 1008/5
jim_thompson5910
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optionally...
y = kx
25 = k*140
25/140 = k
k = 25/140
k = 5/28
--------------------
y = kx
y = (5/28)x
36 = (5/28)*x
36*28 = 5x
1008 = 5x
5x = 1008
x = 1008/5
So x = 1008/5 which is x = 201.6 in decimal form